7th Class Mathematics Exponents and Power Introduction

     Introduction

For any natural number p, the exponent is defined as: \[{{p}^{n}}=p\times p\times p.........\](up to n times), where \[{{p}^{n}}\] is called \[{{n}^{th}}\] power of p and read as "p raised to the power n".  

Write 2401 in exponential form.  

Solution: \[7\times 7\times 7\times 7={{7}^{4}}\]and \[\left( -7 \right)\times \left( -7 \right)\times \left( -7 \right)\times \left( -7 \right)=\left( -7 \right)4.\] Here \[{{7}^{4}}\]and \[{{\left( -7 \right)}^{4}}\]are said to be exponential form of 2401.

Note: \[a{}^\circ =1\]for all rational number 'a', but in the case of negative exponent it is expressed as \[{{(a)}^{-n}}\]and is called the exponent of base "a" is \[-n\]and it can also be defined as \[{{a}^{-n}}=\frac{1}{{{a}^{n}}}.\]